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Characterizing some topological spaces with set-valued maps to a space with an original point 一些具有原点空间集值映射的拓扑空间的特征
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-08 DOI: 10.1016/j.topol.2024.108940
Er-Guang Yang
{"title":"Characterizing some topological spaces with set-valued maps to a space with an original point","authors":"Er-Guang Yang","doi":"10.1016/j.topol.2024.108940","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108940","url":null,"abstract":"<div><p>In this paper, the notion of an original point for a topological space is introduced. Then characterizations of some spaces such as stratifiable spaces and MCP-spaces in terms of set-valued maps with values in <span><math><mi>F</mi><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>, where <em>Y</em> has an original point, are presented.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001251/pdfft?md5=9c66fbb4c11eb98dcb7bfbff9b1e7dec&pid=1-s2.0-S0166864124001251-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140918294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Properties of arithmetics progressions in increasing sequence of T0-topologies on the set of positive integers 正整数集合上 T0 拓扑递增序列中算术级数的性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-07 DOI: 10.1016/j.topol.2024.108939
Dawid Krasiński, Paulina Szyszkowska
{"title":"Properties of arithmetics progressions in increasing sequence of T0-topologies on the set of positive integers","authors":"Dawid Krasiński,&nbsp;Paulina Szyszkowska","doi":"10.1016/j.topol.2024.108939","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108939","url":null,"abstract":"<div><p>In this paper we continue researches deal with increasing sequence <span><math><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-topologies on the set of positive integers focusing on the properties of arithmetic progressions in topologies <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. We characterize the closures of arithmetic progressions in all topologies <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> on <span><math><mi>N</mi></math></span>. Additionally, we present the characterization of the closures of arithmetic progressions in the common division topology <span><math><mi>T</mi></math></span> on <span><math><mi>N</mi></math></span>. Moreover, for each <span><math><mi>m</mi><mo>∈</mo><mi>N</mi></math></span> we characterize regular open arithmetic progressions in <span><math><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math></span> and we examine which of these spaces are semiregular.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016686412400124X/pdfft?md5=e0f5962274f193e430014a7bae207796&pid=1-s2.0-S016686412400124X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the number of nested twice-punctured tori in a hyperbolic knot exterior 论双曲结外部嵌套两次穿刺环的数量
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-07 DOI: 10.1016/j.topol.2024.108938
Román Aranda , Enrique Ramírez-Losada , Jesús Rodríguez-Viorato
{"title":"On the number of nested twice-punctured tori in a hyperbolic knot exterior","authors":"Román Aranda ,&nbsp;Enrique Ramírez-Losada ,&nbsp;Jesús Rodríguez-Viorato","doi":"10.1016/j.topol.2024.108938","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108938","url":null,"abstract":"<div><p>This paper continues a program due to Motegi regarding universal bounds for the number of nonisotopic essential <em>n</em>-punctured tori in the complement of a hyperbolic knot in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. For <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>, Valdez-Sánchez showed that there are at most five nonisotopic Seifert tori in the exterior of a hyperbolic knot. In this paper, we address the case <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>. We show that there are at most six nonisotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracts and retracts by pseudo-deformation of continua without R3-sets, R4-continua, and s-points 不含 R3-集合、R4-连续面和 s-点的连续面伪变形的回缩和回缩
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-03 DOI: 10.1016/j.topol.2024.108937
Félix Capulín, Mario Flores-González , David Maya
{"title":"Retracts and retracts by pseudo-deformation of continua without R3-sets, R4-continua, and s-points","authors":"Félix Capulín,&nbsp;Mario Flores-González ,&nbsp;David Maya","doi":"10.1016/j.topol.2024.108937","DOIUrl":"10.1016/j.topol.2024.108937","url":null,"abstract":"<div><p>A <em>continuum</em> is a nondegenerate, compact, connected, metric space. A topological property <em>P</em> is <em>invariant under retraction</em> provided that each retract of a continuum having <em>P</em> has <em>P</em>, and <em>P</em> is <em>reversible under retraction by pseudo-deformation</em> if the condition a subcontinuum of a continuum <em>X</em> has <em>P</em> implies that <em>X</em> has <em>P</em>. In this paper, we prove that the absence of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>-sets, the absence of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>-continua and the absence of s-points are reversible under retractions by pseudo-deformation, and the absence of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>-sets and the absence of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>-continua are invariant under retractions while the absence of s-points is not.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Vassiliev invariants of virtual knots 论虚结的瓦西里耶夫不变式
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-03 DOI: 10.1016/j.topol.2024.108935
Wout Moltmaker , Louis H. Kauffman
{"title":"On Vassiliev invariants of virtual knots","authors":"Wout Moltmaker ,&nbsp;Louis H. Kauffman","doi":"10.1016/j.topol.2024.108935","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108935","url":null,"abstract":"<div><p>We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in <span>[1]</span>. In particular, following the theory of quantum invariants we work with ‘rotational’ virtual knots. We define chord diagrams, weight systems, and give examples of Lie algebra weight systems of rotational virtual knots. We end with a discussion of extended quantum invariants, which capture information that standard quantum invariants of rotational virtuals cannot.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001202/pdfft?md5=5d5becea01580262505d9d11de7b5df3&pid=1-s2.0-S0166864124001202-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140918295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some topological games involving networks 关于一些涉及网络的拓扑博弈
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-30 DOI: 10.1016/j.topol.2024.108936
Leandro F. Aurichi, Maddalena Bonanzinga, Davide Giacopello
{"title":"On some topological games involving networks","authors":"Leandro F. Aurichi,&nbsp;Maddalena Bonanzinga,&nbsp;Davide Giacopello","doi":"10.1016/j.topol.2024.108936","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108936","url":null,"abstract":"<div><p>In these notes we introduce and investigate two new games called R-nw-selective game and the M-nw-selective game. These games naturally arise from the corresponding selection principles involving networks introduced in <span>[5]</span>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001214/pdfft?md5=9a9dcd38c0f12978b4a664cc0bf36c8d&pid=1-s2.0-S0166864124001214-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140894970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditions for chainability of inverse limits on [0,1] with interval-valued functions [0,1]上带区间值函数的逆极限可链性条件
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-30 DOI: 10.1016/j.topol.2024.108933
M.M. Marsh
{"title":"Conditions for chainability of inverse limits on [0,1] with interval-valued functions","authors":"M.M. Marsh","doi":"10.1016/j.topol.2024.108933","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108933","url":null,"abstract":"<div><p>For an inverse sequence on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with interval-valued functions, we establish necessary conditions on the bonding functions for chainability of the inverse limit space. We also characterize chainability of the inverse limit in this setting in terms of properties of the bonding functions <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and the induced functions <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>→</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></math></span>. The properties, in both cases, are related to how triods arise in the partial graphs associated with the inverse sequence when each graph <span><math><mi>G</mi><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math></span> is chainable.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140894968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong digital topological complexity of digital maps 数字地图的强数字拓扑复杂性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-29 DOI: 10.1016/j.topol.2024.108934
Zhiguo Zhang , Jingyan Li , Jie Wu
{"title":"Strong digital topological complexity of digital maps","authors":"Zhiguo Zhang ,&nbsp;Jingyan Li ,&nbsp;Jie Wu","doi":"10.1016/j.topol.2024.108934","DOIUrl":"10.1016/j.topol.2024.108934","url":null,"abstract":"<div><p>In the paper, we study a digital topological complexity of a digital map and its properties. Firstly, we discuss a strong digital homotopy which allows iterative algorithms based on our previous work. As a generalization of the topological complexity in terms of the strong digital homotopy (we call it strong digital topological complexity), we next study the strong digital <em>f</em>-sectional category of a strong digital fibration. Then we investigate estimates of the upper and lower bounds for the strong digital topological complexity of digital maps. We also reveal the difference between the strong digital topological complexity and the ordinary digital ones. It has shown that the strong digital topological complexity is more similar to the classical continuous case than the ordinary digital ones. Moreover, arising from practical considerations in robotics, we consider the naive digital topological complexity of digital maps.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strongly ultrametric preserving functions 强超对称保值函数
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-25 DOI: 10.1016/j.topol.2024.108931
Oleksiy Dovgoshey
{"title":"Strongly ultrametric preserving functions","authors":"Oleksiy Dovgoshey","doi":"10.1016/j.topol.2024.108931","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108931","url":null,"abstract":"<div><p>An ultrametric preserving function <em>f</em> is said to be strongly ultrametric preserving if ultrametrics <em>d</em> and <span><math><mi>f</mi><mo>∘</mo><mi>d</mi></math></span> define the same topology on <em>X</em> for each ultrametric space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>. The set of all strongly ultrametric preserving functions is characterized by several distinctive features. In particular, it is shown that an ultrametric preserving <em>f</em> belongs to this set iff <em>f</em> preserves the property to be compact.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140902223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterizations of open and semi-open maps of compact Hausdorff spaces by induced maps 用诱导映射表征紧凑 Hausdorff 空间的开映射和半开映射
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-23 DOI: 10.1016/j.topol.2024.108921
Xiongping Dai, Yuxuan Xie
{"title":"Characterizations of open and semi-open maps of compact Hausdorff spaces by induced maps","authors":"Xiongping Dai,&nbsp;Yuxuan Xie","doi":"10.1016/j.topol.2024.108921","DOIUrl":"10.1016/j.topol.2024.108921","url":null,"abstract":"<div><p>Let <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> be a continuous surjection of compact Hausdorff spaces. By<span><span><span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>:</mo><mi>M</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>→</mo><mi>M</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>μ</mi><mo>↦</mo><mi>μ</mi><mo>∘</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace></mspace><mtext> and </mtext><mspace></mspace><msup><mrow><mn>2</mn></mrow><mrow><mi>f</mi></mrow></msup><mo>:</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msup><mo>→</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>Y</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>A</mi><mo>↦</mo><mi>f</mi><mo>[</mo><mi>A</mi><mo>]</mo></math></span></span></span> we denote the induced continuous surjections on the probability measure spaces and hyperspaces, respectively. In this paper we mainly show the following facts:</p><ul><li><span>(1)</span><span><p>If <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> is semi-open, then <em>f</em> is semi-open.</p></span></li><li><span>(2)</span><span><p>If <em>f</em> is semi-open densely open, then <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> is semi-open densely open.</p></span></li><li><span>(3)</span><span><p><em>f</em> is open iff <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>f</mi></mrow></msup></math></span> is open.</p></span></li><li><span>(4)</span><span><p><em>f</em> is semi-open iff <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>f</mi></mrow></msup></math></span> is semi-open.</p></span></li><li><span>(5)</span><span><p><em>f</em> is irreducible iff <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>f</mi></mrow></msup></math></span> is irreducible.</p></span></li></ul></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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